Solve 25a*13a*4a

$$25 a \cdot 13 a \cdot 4 a$$

Evaluate

$$1300a^{3}$$

Solution Steps

Multiply a and a to get a^{2}.

$$25a^{2}\times 13\times 4a$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$25a^{3}\times 13\times 4$$

Multiply 25 and 13 to get 325.

$$325a^{3}\times 4$$

Multiply 325 and 4 to get 1300.

$$1300a^{3}$$

Differentiate w.r.t. a

$$3900a^{2}$$

Steps Using Definition of a Derivative

Multiply a and a to get a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(25a^{2}\times 13\times 4a)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}a}(25a^{3}\times 13\times 4)$$

Multiply 25 and 13 to get 325.

$$\frac{\mathrm{d}}{\mathrm{d}a}(325a^{3}\times 4)$$

Multiply 325 and 4 to get 1300.

$$\frac{\mathrm{d}}{\mathrm{d}a}(1300a^{3})$$

The derivative of ax^{n} is nax^{n-1}.

$$3\times 1300a^{3-1}$$

Multiply 3 times 1300.

$$3900a^{3-1}$$

Subtract 1 from 3.

$$3900a^{2}$$